What is expand ((x^2+7)^2)/(x^5) ?

The solution to expand ((x^2+7)^2)/(x^5) is 1/x+(14)/(x^3)+(49)/(x^5)

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expand ((x^2+7)^2)/(x^5)

expand

\frac{( x ^{2} + 7 ) ^{2}}{x ^{5}}

\frac{1}{x} + \frac{14}{x ^{3}} + \frac{49}{x ^{5}}

Solution steps

\frac{( x ^{2} + 7 ) ^{2}}{x ^{5}}

(x^{2} + 7)^{2} = x^{4} + 14 x^{2} + 49

= \frac{x ^{4} + 14 x ^{2} + 49}{x ^{5}}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{4} + 14 x ^{2} + 49}{x ^{5}} = \frac{x ^{4}}{x ^{5}} + \frac{14 x ^{2}}{x ^{5}} + \frac{49}{x ^{5}}

= \frac{x ^{4}}{x ^{5}} + \frac{14 x ^{2}}{x ^{5}} + \frac{49}{x ^{5}}

Cancel

\frac{x ^{4}}{x ^{5}} : \frac{1}{x}

= \frac{1}{x} + \frac{14 x ^{2}}{x ^{5}} + \frac{49}{x ^{5}}

Cancel

\frac{14 x ^{2}}{x ^{5}} : \frac{14}{x ^{3}}

= \frac{1}{x} + \frac{14}{x ^{3}} + \frac{49}{x ^{5}}

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What is expand ((x^2+7)^2)/(x^5) ?
The solution to expand ((x^2+7)^2)/(x^5) is 1/x+(14)/(x^3)+(49)/(x^5)